共查询到20条相似文献,搜索用时 93 毫秒
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空间曲面上的曲线论是初等微分几何的重要部分.作者提出了一种以外微分运算和向量计算为主要工具,可以进行有关曲面上曲线局部性质的定理机器证明的算法.该算法结合了曲面上的活动标架,曲面上曲线的测地标架和曲线自身的Frenet标架,在Maple 9下得到实现.对20个例子进行的测试表明,由该算法生成的自动证明简短可读. 相似文献
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因其在数字信号处理中的应用潜力,离散Gabor分析引起了不少数学家的关注.讨论了离散周期集上的Gabor系,它可以模拟实际问题中的周期间歇信号.刻画了离散周期集上Gabor系的完备性及Gabor标架;得到了容许完备Gabor系的周期集的一个充分必要条件,并证明此条件也是Gabor集E(即由ХE生成的Gabor系是紧标架)存在的充分必要条件,其证明是构造性的,由此方法可以得到所有由特征函数生成的具有某给定标架界的紧Gabor标架的构造;刻画了容许Gabor Riesz基的周期集;还给出大量例子来说明理论的一般性. 相似文献
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研究了L2(Rd)的有限生成仿射子空间中小波标架的构造.证明了任意有限生成仿射子空间都容许一个具有有限多个生成元的Parseval小波标架,并且得到了仿射子空间是约化子空间的一个充分条件.对其傅里叶变换是一个特征函数的单个函数生成的仿射子空间,得到了与小波标架构造相关的投影算子在傅里叶域上的明确表达式,同时也给出了一些例子. 相似文献
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近似标架是标架的一个推广,近些年引起了一些学者的关注.本文研究近似标架的构造.证明了近似标架在有界满射作用下的像仍是近似标架;给出了近似标架的一些扰动结果;例子表明我们的结果是最优的. 相似文献
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本文利用微积分学隐函数理论,得到曲线一般方程表示下Frenet标架的计算方法,并给出对应Maple源程序. 相似文献
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This paper continues the project, begun in [1], of harmonizing Cartan's classical equivalence method and the modern equivariant moving frame in a framework dubbed involutive moving frames. As an attestation of the fruitfulness of our framework, we obtain a new, constructive and intuitive proof of the Lie-Tresse theorem (Fundamental basis theorem) and a first general upper bound on the minimal number of generating differential invariants for Lie pseudo-groups. Further, we demonstrate the computational advantages of this framework by studying the equivalence problem for first order PDE in two independent variables and one dependent variable under point transformations. 相似文献
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Bourbaki's extension theorem (General Topology, Part 1, I, 8.5) is known to be one of the most important results concerning the extension of continuous maps. This paper presents a pointfree generalization of this together with various applications to illustrate its remarkable usefulness. 相似文献
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With the aim of understanding the mathematical structure of the fluctuation-dissipation theorem in non-equilibrium statistical physics and then constructing a mathematical principle in the modeling problem for time series analysis, we have developed the theory of KM2O-Langevin equations for discrete time stochastic processes. In this paper, as a new method for model analysis in the theory of KM2O-Langevin equations, we show that block frames provide a natural mathematical language for dealing with minimum norm expansions of multi-dimensional stochastic processes which do not necessarily satisfy stationarity and non-degeneracy conditions. 相似文献
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在Hilbert C~*-模框架下,给出了闭子模之间的酉等价与相应的遗传C~*-子代数的*同构,及对应的开投影的等价性的关系定理. 相似文献
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The sampling problem on a closed subspace Vo of L2(ℝ) is studied. For the regular sampling, a necessary and sufficient condition on the sampling theorem is presented and the
sampling problem proposed by Walter is completely solved. Moreover, a representation formula for the derived function is given.
The irregular sampling is studied. The results improve the ones of Walter and Liu’s.
Project supported by the National Natural Science Foundation of China (Grant No. 16971047). 相似文献
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Ahmed I. Zayed 《Proceedings of the American Mathematical Society》1996,124(12):3767-3776
An analog of the Whittaker-Shannon-Kotel'nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. One of the consequences of this theorem is that it allows us to derive sampling theorems associated with boundary-value problems and some homogeneous integral equations, which in turn gives us a generalization of another sampling theorem by Kramer.
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Zhijing Zhao 《Numerical Functional Analysis & Optimization》2013,34(11-12):1394-1407
Finding verifiable conditions for wavelet systems to be wavelet frames is among the core problems in wavelet analysis. In this paper, we give some simple and sufficient conditions that ensure a multidimensional irregular wavelet system to be a frame or a weighted frame. Quantitative results are provided, and explicit frame bounds are given. 相似文献
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ON THE STABILITY OF FUSION FRAMES (FRAMES OF SUBSPACES) 总被引:1,自引:0,他引:1
Mohammad Sadegh Asgari 《数学物理学报(B辑英文版)》2011,31(4):1633-1642
A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame (frame of subspaces) is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3(iii)] with extra information about the bounds. 相似文献
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Banach frames and atomic decompositions are sequences that have basis-like properties but which need not be bases. In particular, they allow elements of a Banach space to be written as linear combinations of the frame or atomic decomposition elements in a stable manner. In this paper we prove several functional — analytic properties of these decompositions, and show how these properties apply to Gabor and wavelet systems. We first prove that frames and atomic decompositions are stable under small perturbations. This is inspired by corresponding classical perturbation results for bases, including the Paley — Wiener basis stability criteria and the perturbation theorem el kato. We introduce new and weaker conditions which ensure the desired stability. We then prove quality properties of atomic decompositions and consider some consequences for Hilbert frames. Finally, we demonstrate how our results apply in the practical case of Gabor systems in weighted L2 spaces. Such systems can form atomic decompositions for L2w(IR), but cannot form Hilbert frames but L2w(IR) unless the weight is trivial. 相似文献